High-order discontinuous Galerkin method for elastohydrodynamic lubrication line contact problems

SUMMARYThe use of an adjoint technique for goal-based error estimation described by Hart et al. (Int. J. Numer. Meth. Fluids 2005; 47:1069-1074) is extended to the numerical solution of free boundary problems that arise in elastohydrodynamic lubrication (EHL). EHL systems are highly nonlinear and consist of a thinfilm approximation of the flow of a non-Newtonian lubricant which separates two bodies that are forced together by an applied load, coupled with a linear elastic model for the deformation of the bodies. A finite difference discretization of the line contact flow problem is presented, along with the numerical evaluation of an exact solution for the elastic deformation, and a moving grid representation of the free boundary that models cavitation at the outflow in this one-dimensional case. The application of a goal-based error estimate for this problem is then described. This estimate relies on the solution of an adjoint problem; its effectiveness is demonstrated for the physically important goal of the total friction through the contact. Finally, the application of this error estimate to drive local mesh refinement is demonstrated.

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“…Recently, higher order alternatives have been proposed, e.g. [20], however these have yet to be widely used in practice.…”

Section: Discretizationmentioning

confidence: 98%

Using adjoint error estimation techniques for elastohydrodynamic lubrication line contact problems

Hart

Berzins

Goodyer

et al. 2010

Numerical Methods in Fluids

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“…The corresponding formulation for the Reynolds equation has been introduced by Lu et al [14], following the work of Baumann and Oden [4], and reads…”

Section: Finite Element Treatmentmentioning

confidence: 99%

“…It is clear that the Reynolds equation in the form (14) states that the flux q given by the term in brackets is constant along the lubricated boundary. It is also seen that at the points of zero pressure gradient (e.g.…”

Section: Reynolds Equationmentioning

confidence: 99%

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Finite element treatment of soft elastohydrodynamic lubrication problems in the finite deformation regime

Stupkiewicz

2009

Comput Mech

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Soft elastohydrodynamic lubrication (EHL) problem is studied for a reciprocating elastomeric seal with full account of finite configuration changes. The fluid part is described by the Reynolds equation which is formulated on the deformed boundary of the seal treated as a hyperelastic body. The paper is concerned with the finite element (FE) treatment of this soft EHL problem. Displacement-based FE discretization is applied for the solid part. The Reynolds equation is discretized using the FE method or, alternatively, the discontinuous Galerkin method, both employing higherorder interpolation of pressure. The performance of both methods is assessed by studying convergence and stability of the solution for a benchmark problem of an O-ring seal. It is shown that the solution may exhibit spurious oscillations which occur in severe lubrication conditions. Mesh refinement results in reduction of these oscillations, while increasing the pressure interpolation order or application of the discontinuous Galerkin method does not help significantly.

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“…k is called degrees of freedom (DOFs), and k (r ) the nodal basis function. In terms of the finite element, basis function can be linear, quadratic, cubic or even higher order [25,26]. In this paper, we construct piecewise continuous basis functions by using Lagrange interpolation.…”

Section: High-order Basis Functionsmentioning

confidence: 99%

A new numerical method for BLT forward problem based on high‐order finite elements

Hou¹,

Tian²,

Wu³

et al. 2008

Commun. Numer. Meth. Engng.

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SUMMARYMolecular imaging possesses the ability to characterize and measure biological processes at the cellular and molecular level in vivo. As one of the new molecular imaging modalities, bioluminescence tomography (BLT) is to reconstruct the light distribution inside a small animal from the photon flux measured on its surface. To obtain accurate and robust reconstruction, it needs a good understanding of the propagation of photons in biological tissues, which is referred to as the forward problem in BLT. Because the turbid media is high scattering and low absorption, the propagation process can be described by the steady diffusion equation. In this paper, an hp-adaptivity method for BLT forward problem is presented based on finite elements of high orders and moderate meshes by finite element method (FEM). Both numerical simulation and physical experiment are performed to evaluate the accuracy of solution and the efficiency of computation. The relevant results show that element order is more critical than mesh size to produce an accurate FEM solution efficiently.

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High-order discontinuous Galerkin method for elastohydrodynamic lubrication line contact problems

Cited by 25 publications

References 21 publications

Using adjoint error estimation techniques for elastohydrodynamic lubrication line contact problems

Using adjoint error estimation techniques for elastohydrodynamic lubrication line contact problems

Finite element treatment of soft elastohydrodynamic lubrication problems in the finite deformation regime

A new numerical method for BLT forward problem based on high‐order finite elements

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